Finite Group Databasebeta

← #24999342

Subgroups — #24999342

Order 11008.

516 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145741C211yesmaximal, characteristic
2#19145545C211yesmaximal, characteristic
3#19142973C211yesmaximal, characteristic
4#19135572C211yesmaximal, characteristic
5#19133275C211yesmaximal, characteristic
6#19133266C211yesmaximal, characteristic
7C43×#1276C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×#13063325C2211yescharacteristic
10C2×#13063325C2211yescharacteristic
11#14583297—21no—
12#14583279—21no—
13#14583250—21no—
14#14583250—21no—
15#14583230—22no—
16#14583185—22no—
17#14583110—22no—
18#14583057—22no—
19#14582923C2211yescharacteristic
20#14582805—22no—
21#14582805—22no—
22#14582765—22no—
23#14582659—22no—
24#14582647—22no—
25#14582644—22no—
26C43×#431C2211yescharacteristic
27C43×#431C2211yescharacteristic
28C43×C43C2211yescharacteristic
29C22×Dic86—21no—
30C22×Dic86D412yes—
31C2×Dic172—24no—
32C2×#10621877—21no—
33#13063325—21no—
34#13063325—21no—
35#13063325—21no—
36#13063325—21no—
37#13063325—21no—
38#13063325—21no—
39#13063325—21no—
40#13063325—21no—
41#13063325D411yescharacteristic
42#13063325D411yescharacteristic
43#13063317—21no—
44#13063304—21no—
45#13063304—21no—
46C4×Dic86—21no—
47C4×Dic86—21no—
48#13063284—21no—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43D412yes—
53#13063257—24no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)—21no—
56#13063250—24no—
57#13063250—24no—
58C43⋊#95—28no—
59C2×C42×C43—21no—
60C2×C42×C43—21no—
61C2×C42×C43D412yes—
62C2×C42×C43C2311yescharacteristic
63C4⋊C8×C43D412yes—
64C4⋊C8×C43D412yes—
65C22⋊C8×C43—21no—
66C22⋊C8×C43—21no—
67C4×C8×C43—21no—
68C4×C8×C43—21no—
69C22×C4×C43—22no—
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—22no—
74C22×Dic43—22no—
75C2×Dic86—21no—
76C2×Dic86—22no—
77C2×Dic86—21no—
78C2×Dic86—22no—
79C2×Dic86—44no—
80C2×Dic86—41no—
81C2×Dic86—41no—
82C2×Dic86—42no—
83C2×Dic86—42no—
84C2×C8×C43—22no—
85C2×C8×C43—22no—
86C42×C43—24no—
87C42×C43—22no—
88C42×C43—22no—
89C42×C43—42no—
90C42×C43C2×D411yescharacteristic
91C42×C43C2×D411yescharacteristic
92C42×C43C2×D411yescharacteristic
93C42×C43#4111yescharacteristic
94C22⋊Dic43—41no—
95C4⋊Dic43—21no—
96C4⋊Dic43—22no—
97C4⋊Dic43—21no—
98C4⋊Dic43—22no—
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43—41no—
102C4⋊Dic43—41no—
103C4⋊Dic43—41no—
104C4⋊Dic43—41no—
105C4⋊Dic43—41no—
106C4⋊Dic43—41no—
107Dic43⋊C4—41no—
108Dic43⋊C4—41no—
109C4×Dic43—41no—
110#10621877—42no—
111C2×C43⋊C8—41no—
112Dic172—84no—
113C23×C43#12011yescharacteristic
114C2×C4×C43—22no—
115C2×C4×C43—22no—
116C2×C4×C43—24no—
117C2×C4×C43—42no—
118C2×C4×C43—42no—
119C2×C4×C43#12011yescharacteristic
120C2×C4×C43#12011yescharacteristic
121C2×C4×C43#12111yescharacteristic
122C2×C4×C43#12111yescharacteristic
123C2×C4×C43#12111yescharacteristic
124C2×C4×C43#12711yescharacteristic
125C2×C4×C43#13512yes—
126C2×C4×C43#13712yes—
127C2×Dic43—44no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—42no—
131C2×Dic43—42no—
132C2×Dic43—44no—
133Dic86—42no—
134Dic86—44no—
135Dic86—42no—
136Dic86—82no—
137Dic86—81no—
138Dic86—81no—
139Dic86—82no—
140C8×C43—42no—
141C8×C43—42no—
142C43⋊C8—81no—
143#10298—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43#39211yescharacteristic
147C22×C43#45212yes—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—44no—
151C4×C43#45512yes—
152C4×C43#45612yes—
153C4×C43#46412yes—
154C4×C43#49511yescharacteristic
155C4×C43#49711yescharacteristic
156Dic43—82no—
157Dic43—81no—
158Dic43—81no—
159Dic43—82no—
160#3229—431no—
161#3209—431no—
162#2862—431no—
163#1994—431no—
164#1548—431no—
165#1546—431no—
166#1276D4311yescharacteristic
167C2×C43—22no—
168C2×C43#200411yescharacteristic
169C2×C43#200511yescharacteristic
170C2×C43#201511yescharacteristic
171#533—431no—
172C2×C4⋊Q8—431no—
173C2×C4⋊Q8—431no—
174#498—861no—
175#494—861no—
176#487—861no—
177#487—861no—
178#483—862no—
179#475—862no—
180#462—862no—
181#451—862no—
182#431C2×D4311yescharacteristic
183#431C2×D4311yescharacteristic
184#423—431no—
185#391—862no—
186#391—862no—
187#382—862no—
188C43C2×D4311yescharacteristic
189#339—862no—
190#333—862no—
191#332—862no—
192C43#1029811yescharacteristic, complemented, Sylow
193C22×Q8—432no—
194C22×Q8—861no—
195C2×Q16—864no—
196C2×M16—861no—
197C4⋊Q8—431no—
198C4⋊Q8—431no—
199C4⋊Q8—861no—
200C4⋊Q8—861no—
201C4⋊Q8—861no—
202C4⋊Q8—861no—
203C4⋊Q8—861no—
204C4⋊Q8—861no—
205C4⋊Q8—861no—
206C4⋊Q8—861no—
207#125—861no—
208C22⋊Q8—861no—
209C22⋊Q8—861no—
210C4×Q8—861no—
211C4×Q8—861no—
212#117—861no—
213C2×C4⋊C4—432no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42D17212yes—
220C2×C42C22×D4311yescharacteristic
221#106—864no—
222C4⋊C8—861no—
223C4⋊C8—861no—
224C4⋊C8D17212yes—
225C4⋊C8D17212yes—
226#103—864no—
227#103—864no—
228C22⋊C8—21no—
229C22⋊C8—21no—
230C4×C8—21no—
231C4×C8—21no—
232#95—868no—
233C2×Q8—861no—
234C2×Q8—862no—
235C2×Q8—861no—
236C2×Q8—862no—
237C2×Q8—1724no—
238C2×Q8—1721no—
239C2×Q8—1721no—
240C2×Q8—1722no—
241C2×Q8—1722no—
242C22×C4—22no—
243C22×C4—862no—
244C22×C4—862no—
245C22×C4C2×D17211yescharacteristic
246C22×C4D4×D4311yescharacteristic
247C22×C4D4×D4311yescharacteristic
248Q16—3444no—
249M16—1722no—
250C2×C8—22no—
251C2×C8—22no—
252C2×C8—1721no—
253C4⋊C4—861no—
254C4⋊C4—862no—
255C4⋊C4—861no—
256C4⋊C4—862no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—1721no—
260C4⋊C4—1721no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C22⋊C4—1721no—
268C42—24no—
269C42—22no—
270C42—22no—
271C42—42no—
272C42—1721no—
273C42C2×D17211yescharacteristic
274C42C2×D17211yescharacteristic
275C42D4×D4311yescharacteristic
276C42#1062190211yescharacteristic
277C23#1306329511yescharacteristic
278Q8—3442no—
279Q8—3442no—
280Q8—3441no—
281Q8—3441no—
282Q8—1722no—
283Q8—1724no—
284Q8—1722no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—1724no—
291C2×C4—1724no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1722no—
295C2×C4—1722no—
296C2×C4#1306329511yescharacteristic
297C2×C4#1306329511yescharacteristic
298C2×C4#1306330011yescharacteristic
299C2×C4#1306330011yescharacteristic
300C2×C4#1306330011yescharacteristic
301C2×C4#1306332211yescharacteristic
302C2×C4#1306334712yes—
303C2×C4#1306335812yes—
304C8—42no—
305C8—42no—
306C8—3441no—
307C22—21no—
308C22—21no—
309C22#1458280911yescharacteristic
310C22#1458306312yes—
311C4—21no—
312C4—21no—
313C4—44no—
314C4—3442no—
315C4—3441no—
316C4—3441no—
317C4—3442no—
318C4#1458307812yes—
319C4#1458308312yes—
320C4#1458312212yes—
321C4#1458328311yescharacteristic
322C4#1458329311yescharacteristic
323C2—22no—
324C2#1913562711yescharacteristic
325C2#1913563411yescharacteristic
326C2#1913569211yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1276C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#1276D43
hypocenterC43#10298
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
192. C43#10298semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191457412
#191455452
#191429732
#191355722
#191332752
#191332662
C43×#12762
#1029843